Kernel Clustering: Density Biases and Solutions.

Area of Science:

• Machine Learning
• Data Mining
• Computational Statistics

Background:

• Kernel methods are widely used in clustering for their flexibility and power.
• Existing kernel clustering algorithms can exhibit density biases, causing practical issues.
• These biases, like Breiman's bias, affect clustering outcomes in real-world data.

Purpose of the Study:

• To theoretically analyze and identify density biases in popular kernel clustering criteria.
• To propose principled solutions for mitigating density biases in kernel clustering.
• To demonstrate the effectiveness of density equalization in improving clustering performance.

Main Methods:

• Formal theoretical analysis of kernel clustering criteria.
• Identification and classification of density biases (e.g., density mode isolation, sparsest subset bias).
• Development of density equalization strategies using locally adaptive weights or kernels.

Main Results:

• Demonstrated density mode isolation bias in kernel K-means and related biases in other methods.
• Showed that density equalization effectively addresses data inhomogeneity.
• Found that density equalization unifies several popular kernel clustering objectives.

Conclusions:

• Density biases are a significant limitation in many kernel clustering methods.
• Density equalization offers a principled and effective solution to these biases.
• Understanding and addressing density biases is crucial for reliable data analysis across disciplines.